System of equations: \(\begin{cases} 5u - 2v + 1 = 4(2u - v) \\ 0.2(4u + v) + 0.5 = 0.5(2u + 1) \end{cases}\)

System of equations:

• Equation 1: \( 5u - 2v + 1 = 4(2u - v) \)
• Equation 2: \( 0.2(4u + v) + 0.5 = 0.5(2u + 1) \)

Step-by-step solution:

1. Simplify Equation 1:
   \( 5u - 2v + 1 = 8u - 4v \)
   Rearrange terms to group 'u' and 'v':
   \( -3u + 2v = -1 \) (Equation 1 simplified)
2. Simplify Equation 2:
   Multiply both sides by 10 to eliminate decimals:
   \( 2(4u + v) + 5 = 5(2u + 1) \)
   \( 8u + 2v + 5 = 10u + 5 \)
   Rearrange terms:
   \( -2u + 2v = 0 \) (Equation 2 simplified)
3. Solve the system of simplified equations:
   We have:
   \( -3u + 2v = -1 \)
   \( -2u + 2v = 0 \)
   Subtract the second simplified equation from the first:
   \( (-3u + 2v) - (-2u + 2v) = -1 - 0 \)
   \( -3u + 2v + 2u - 2v = -1 \)
   \( -u = -1 \)
   \( u = 1 \)
4. Substitute the value of 'u' into the second simplified equation to find 'v':
   \( -2(1) + 2v = 0 \)
   \( -2 + 2v = 0 \)
   \( 2v = 2 \)
   \( v = 1 \)

Answer: u = 1, v = 1